Question

Уравнение - 4^(-x+0,5) - 7*2^-x - 4 < 0

Answer 1

$2 cdot 4^{-x}-7 cdot 2^{-x}-4 textless 0 \ 2^{-x} =t \ begin{cases} t textgreater 0 \2t^2-7t-4 textless 0 end{cases} textless = textgreater begin{cases} t textgreater 0 \(2t+1)(t-4) textless 0 end{cases} textless = textgreater begin{cases} t textgreater 0 \ - frac{1}{2} textless t textless 4 end{cases} \ \ = textgreater 0 textless t textless 4 \ \ 2^{-x} textless 4\ -x textless 2\ x textgreater -2 = textgreater boxed{x in (-2; + infty)}$